The plane strain model of a rigid building foundation embedded below the surface of an elastic half space is treated. The foundation is assumed to be vibrating freely with arbitrary transient time-dependences U(t) and V(t) in the horizontal and vertical directions, respectively, and to be rocking about its mass center with magnitude Ω(t). The total restraining reactions exerted upon the foundation by the surrounding medium are determined exactly during the initial time period for a P-wave to traverse the foundation base width. Thereafter the results become approximate. In this manner the coupled equations of motion for free vibrations of the foundation are obtained. A numerical example presents the impulse response matrix for U, V, and Ω. Peak responses are found to occur during the early time period where the results are exact.
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September 1974
Research Papers
Coupled Rocking and Translating Vibrations of a Buried Foundation
S. A. Thau,
S. A. Thau
Department of Mechanics and Mechanical and Aerospace Engineering, Illinois Institute of Technology, Chicago, Ill.
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A. Umek
A. Umek
Department of Mechanics and Mechanical and Aerospace Engineering, Illinois Institute of Technology, Chicago, Ill.
Search for other works by this author on:
S. A. Thau
Department of Mechanics and Mechanical and Aerospace Engineering, Illinois Institute of Technology, Chicago, Ill.
A. Umek
Department of Mechanics and Mechanical and Aerospace Engineering, Illinois Institute of Technology, Chicago, Ill.
J. Appl. Mech. Sep 1974, 41(3): 697-702 (6 pages)
Published Online: September 1, 1974
Article history
Received:
December 1, 1973
Revised:
January 1, 1974
Online:
July 12, 2010
Citation
Thau, S. A., and Umek, A. (September 1, 1974). "Coupled Rocking and Translating Vibrations of a Buried Foundation." ASME. J. Appl. Mech. September 1974; 41(3): 697–702. https://doi.org/10.1115/1.3423374
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